Unlike scientific or factual arguments, where the best positions are those with the best supporting evidence, moral arguments by their very nature cannot be based upon objective verifiable measurements. Almost every time I see an argument where morality is brought up, it becomes a contest of opinions.
First you must assess if the conversation will be civil, respectful of everyones opinion and time is not rushed. Talking in turns, for example, will help here.
Second, a clear value system must be put in place to weigh the arguments i.e. reducing human suffering/life, environmental impact, future generations, freedom of expression, human rights, etc...
lastly, lots of alcohol to loosen inhibition (wink!)
I think the key word is argument. As the quote says, it is better to be silent and be thought a fool than to open your mouth and confirm it. Most people who want to argue their perceptions/morality are doing it more so to convince themselves than someone else. There are some very useful counseling techniques that work very well with people who want to argue, such as letting them “run the tape out”, parroting, summarizing, and active listening. Let them keep talking until they exhaust themselves and they usually say something foolish to get you to engage.
Love this quote by George Bernard Shaw:
I learned long ago not to wrestle with a pig. You get dirty, and besides, the pig likes it.
Argue on the basis of hurting or not hurting people. If they try to drag it back to religion, just say you don't want to hear what they think god says, but what they have to say. Sometimes, it's a struggle to keep the conversation on track. (I'm in a closed argument group on fb, and some people think that name slinging is a good way to argue, and another just give the name slingers a hug meme. They catch on fast.)
Morality largely IS a contest of opinions because most "morals" are culturally constructed - Think about the idea of "walking marriages" where the "marriage" is basically a convenient sexual relationship...
In other words, If I were to tell you that for me I have guys over for sex and then send them away at sunrise - My brothers live with me and take care of my kids while I work... My babies have never really met their fathers, of whom there might be many... I would likely be called immoral. If I were Mosuo, however, I would just be a regular woman.
Just live your life by treating others with Kindness and Respect. That in itself will diminish any argument against your morals. Conversely, it will strengthen your argument against those that would fault you for not being with their god. If they bring their god into the argument by saying whay he said, remind them that you're not interested in what their imaginary friend has to say, but what they have to say.